The LinGO Grammar Matrix provides a foundation for building grammars of natural languages in HPSG. It includes a web-based questionnaire that allows a linguist to describe a natural language, and then creates a starter grammar for that language based on the answers. In this dissertation, I describe improvements I have made to the typological coverage of this system, including support for core case marking, agreement in person, number, and gender, direct-inverse languages, and a lexicon containing an arbitrarily large number of lexical types, lexical items, and inflectional morphemes.